In the tie sewing machines hitherto in use, because of the varying width of the tie cut-out over the length of the tie cut-out (in accordance with the divergent edges of the finished tie), the latter is pressed into a folding slit to different depths during the folding operation in order to obtain a substantially constant height of the edges of the tie cut-out projecting from the slit at the end of this operation. This different depth of pressing in is brought about in that the slit is given a corresponding depth profile along its length. Individual folding bars of a folding sword, which descend into the slit under the action of the force of gravity as a result of their weight, then press the tie cut-out down to the bottom of the slit in each case, where the individual folding bars are stopped. When the tie sewing machine in question has to be converted from one shape of tie to another, a correspondingly profiled bottom has to be inserted in the slit each time. This means that, according to the number of tie shapes to be produced, a corresponding number of bottom profiles for the slit must be available.